Interhemispheric anatomical asymmetries have long been thought to be related to language lateralisation. Previous studies have explored whether asymmetries in the diffusion characteristics of white matter language tracts are consistent with language lateralisation. These studies, typically with smaller cohorts, yielded mixed results. This study investigated whether connectomic analysis of quantitative anisotropy (QA) and shape features of white matter tracts across the whole brain are associated with language lateralisation. We analysed 1040 healthy individuals from the Human Connectome Project database. Hemispheric language dominance for each participant was quantified using a laterality quotient (LQ) derived from fMRI activation in regions of interest (ROIs) associated with a language comprehension task compared against a math task. A linear regression model was used to examine the relationship between structural asymmetry and functional lateralisation. Connectometry revealed that LQs were significantly negatively correlated with QA of corpus callosum tracts, including forceps minor, body, tapetum, and forceps major, indicating that reduced language dominance (more bilateral language representation) is associated with increased QA in these regions. The QA of the left arcuate fasciculus, cingulum, and right cerebellar tracts was positively associated with LQ, suggesting that stronger structural asymmetry in these tracts may identify left language dominance. Language lateralisation was not significantly associated with the shape metrics (including length, span, curl, elongation, diameter, volume, and surface area) of all white matter tracts. These results suggest that diffusion measures of microstructural architecture, and not the geometric features of reconstructed white matter tracts, are associated with lateralisation of language comprehension functions. People with increased dependence on both cerebral hemispheres for language processing may have more developed commissural fibres, which may support more efficient interhemispheric communication.